Endomorphism rings of modules whose cardinality is cofinal to omega
Rings and Algebras
2007-05-23 v1 Logic
Abstract
The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^{aleph_0}<lambda<=2^mu. If A is aleph_0-cotorsion-free or A is countably free, respectively, then there exists an aleph_0-cotorsion-free or a separable (reduced, torsion-free) R-module G respectively of cardinality |G|=lambda with End_RG=A oplus Fin G.
Cite
@article{arxiv.math/0011186,
title = {Endomorphism rings of modules whose cardinality is cofinal to omega},
author = {Rüdiger Göbel and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0011186},
year = {2007}
}